You Do Need power plug adapter while traveling from Pitcairn Islands to Ecuador.

Here is Why You Need An Adapter

The outlet and plug type used in Ecuador are A and B and in Pitcairn Islands is I. This is how they look like.

Pitcairn Islands

In Pitcairn Islands, outlets of type I are in use.

Type I

Ecuador

In Ecuador, outlets of type A and B are in use.

Type A

Type B